Problem: Simplify the following expression: $ n = \dfrac{-5}{x - 1} - 7 $
Solution: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{x - 1}{x - 1}$ $ \dfrac{-7}{1} \times \dfrac{x - 1}{x - 1} = \dfrac{-7x + 7}{x - 1} $ Therefore $ n = \dfrac{-5}{x - 1} + \dfrac{-7x + 7}{x - 1} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-5 - 7x + 7}{x - 1} $ $n = \dfrac{-7x + 2}{x - 1}$